This thesis presents the first results of efforts at improving the radiation hydrodynamic description of classical novae with HYDRA, a 1-D, Lagrangian hydrodynamics code developed specifically for this project. After reviewing the architecture and performance of HYDRA, we proceed to apply it to three different problems of classical nova evolution. The first of these is the modeling of the early super-Eddington phase of fast classical novae. We find that the necessary conditions for achieving super-Eddington luminosities of any duration are identical to those believed necessary for achieving rapid evolution of the lightcurve, but we find that additional physics describing the level of coupling between the material and radiation is needed to model this phenomenon correctly. We identify in particular the need to distinguish between absorption and scattering processes in the modeling of energy and momentum exchange between the material and radiation. The second problem is the investigation of spectral line driven mass loss as an expedient to the post-maximum decline of classical novae. We find that the effects of line driving at early times are dwarfed by the effects of improved numerical resolution of the expanding envelope. Even with enhancements in the total amount of mass ejected, however, we see that early mass loss rates are insufficient to drive a rapid decline in the visual lightcurve, owing to the remarkably small amount of residual mass needed to define an optically bright photosphere. This result places the effects of common envelope evolution in an even more important light. The third problem is the use of the formal solution to the transfer equation to compute U, B, and V lightcurves of model novae, and also to compute synthetic spectral continua covering six decades in wavelength. The initial formulation of this technique is fairly crude, although some effects of atmospheric extension upon the spectral evolution are clearly visible, and consistent with similar work done for the spectra of early-type stars.